Collision Theories of Pressure Broadening of Spectral Lines

It is shown that in the calculation of absorption in the Lorentz collision theory, it is essential to include the work done impulsively by the electric field during the sudden changes of position at collision. This work was implicitly included in the theory of Van Vleck and Weisskopf, but these authors did not give the breakdown into work done between and at collision. It is verified that the shapes of spectral lines for a classical harmonic oscillator and also a Debye slow rotator are the same in absorption and spontaneous emission, provided the energy density obeys the Rayleigh-Jeans law. The usual proofs of equilibrium simply establish equality of the integrated absorption and emission, without examining the detailed balancing at individual frequencies, not necessarily near resonance.